What is the significance of the N.A. number inscribed on the outer barrel of an objective?
This number is the numerical aperture of the objective, a measure of the light-gathering capacity of the objective. The higher the numerical aperture, other things being equal, the better the objective is able to separate the details of the specimen in forming an image; also the brighter the image. Higher N.A. objectives are usually more expensive. The higher the numerical aperture of the objective, the shallower the depth of field (see definition of depth of field).